This is basically a matter of pulling together the necessary concepts at different levels of scientific plausibility.
Assume your villain is a normal living, breathing, walking, talking, thinking and feeling human being. That's step one.
Steps two and three involves (a) providing a source for the radiation and, (b) a way of protecting a human being from high level radiation.
This suggests something science-fictional, for example, a force-field. OK. Let's assume the villain has a force-field surrounding his body. This only needs to reach a miniscule distance from the surface of his skin.
The force-field will have two functions. Firstly, it draws virtual photons and particles from the quantum vacuum and at the same time prevents from disappearing back into the quantum vacuum. This will have the effect of generating radiation, i.e., he will radiate in all directions perpendicular tot he surface of his force-field. This a variant on the concept of Hawking radiation.
Because the villain is living inside a permanent force-field, this will act as a perfect barrier to the radiation generated by his force-field. It could do this by either being totally impervious to all forms of radiation or acts as a perfect mirror or reflector to all forms of radiation. It could also act as perfect sink causing all forms of radiation to be transferred into the quantum vacuum before it can reach him or his body.
Considering the villain, operating under this concept, will have one small problem. Namely, eating and drinking or even inhaling air. Everything passing through the thin layer of his force-field will be irradiated. So he's eating, drinking and breathing radioactive matter.
Luckily if the force-field acts as a perfect sink for all radiation, sending it into the quantum vacuum, the villain won't be bothered by ingesting or inhaling anything radioactive. Any radiation will simply disappear into the quantum vacuum before it can interact with the matter constituting his body.